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Interior $C^{1,\alpha}$ regularity for infinity-harmonic functions

Proves uniform interior

C^{1,\alpha_d}

regularity for bounded infinity-harmonic functions in every dimension d ≥ 3, for a positive exponent depending only on dimension. The gradient's supremum norm and Hölder seminorm on the half unit ball are bounded by a dimension-dependent constant times the oscillation on the unit ball. The exponent is not explicit.

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Uniform Interior $C^{1,\alpha}$ Estimates for Infinity-Harmonic Functions

Oct 4, 2026·interior-c1-infinity-harmonic.pdf

We prove a uniform interior

C^{1,\alpha_d}

estimate for bounded infinity-harmonic functions in every dimension d ≥ 3. For some

\alpha_d\in(0,1/3]

depending only on the dimension, the gradient's supremum norm and α

_{d}

-Hölder seminorm on B

_{1/2}

are bounded by a dimension-dependent constant times the oscillation on B

_{1}

. The exponent is not explicit, and no endpoint or boundary regularity claim is made. In particular, infinity-harmonic functions are locally C

^{1}

on every open subset of ℝ

^{d}

, for d ≥ 3.

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Interior C1,αC^{1,\alpha}C1,α regularity for infinity-harmonic functions

Manuscripts in this family · 1

Uniform Interior C1,αC^{1,\alpha}C1,α Estimates for Infinity-Harmonic Functions

Interior $C^{1,\alpha}$ regularity for infinity-harmonic functions

Uniform Interior $C^{1,\alpha}$ Estimates for Infinity-Harmonic Functions